To determine which falling object will result in the least kinetic energy when it collides with the ground, we can use the formula for kinetic energy (KE):
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is the mass of the object in kilograms
- \( v \) is the velocity of the object in meters per second
Now, let's calculate the kinetic energy for each option:
1. **100 grams of water falling at 10 m/s**
- Mass = 0.1 kg, Velocity = 10 m/s
- \( KE = \frac{1}{2} (0.1)(10^2) = 0.5 \times 0.1 \times 100 = 5 \, \text{Joules} \)
2. **10 grams of water falling at 1 m/s**
- Mass = 0.01 kg, Velocity = 1 m/s
- \( KE = \frac{1}{2} (0.01)(1^2) = 0.5 \times 0.01 \times 1 = 0.005 \, \text{Joules} \)
3. **10 grams of dirt falling at 2 m/s**
- Mass = 0.01 kg, Velocity = 2 m/s
- \( KE = \frac{1}{2} (0.01)(2^2) = 0.5 \times 0.01 \times 4 = 0.02 \, \text{Joules} \)
4. **100 grams of dirt falling at 15 m/s**
- Mass = 0.1 kg, Velocity = 15 m/s
- \( KE = \frac{1}{2} (0.1)(15^2) = 0.5 \times 0.1 \times 225 = 11.25 \, \text{Joules} \)
Based on these calculations, the object that results in the least kinetic energy when it collides with the ground is:
**10 grams of water falling at 1 m/s (0.005 Joules).**